Senators on Tuesday announced a breakthrough in a long-stalled bipartisan effort to advance sweeping sanctions against Russia, paving the way for an evening test vote on the compromise bill after the Washington funeral of Senator Lindsey Graham, its main champion.

Republicans and Democrats said they had addressed concerns from members of both parties and were ready to push ahead in efforts to pass the measure in honor of Mr. Graham, who spent the final hours of his life working in Ukraine to cement it.

The measure would impose harsh new penalties on countries that purchase oil and other energy products from Russia, as well as extend existing sanctions against Iran seeking to limit its ability to fuel its wartime economy.

“We are proud to announce an agreement on legislation to stop purchasers of Russian oil and gas from fueling Putin’s war machine and to continue restricting the Iranian regime’s ability to support terrorism and build its nuclear program,” said a joint statement from the Republican senators Darline Graham of South Carolina, Jim Risch of Idaho, Roger Wicker of Mississippi and Katie Britt of Alabama and the Democratic senators Richard Blumenthal of Connecticut and Jeanne Shaheen of New Hampshire. “There is no greater way to honor Senator Graham’s legacy than to move forward with this bipartisan agreement, and we look forward to today’s vote.”

The announcement came just as lawmakers and his family gathered at the Capitol to honor Mr. Graham’s life, and hours before the president and world leaders convened at the National Cathedral for his funeral.

An initial vote was expected on Tuesday evening, just after President Volodymyr Zelensky of Ukraine, who has long pressed for such a sanctions package, was to meet with senators on Capitol Hill.

The revised legislation reflects an intense round of negotiations to narrow the measure’s provisions and ensure tighter congressional oversight over the penalties it would impose.

To appease Democrats who had balked at handing President Trump new tariff authority, the revised measure would require that the president impose the sanctions rather than simply permit him to do so — though Mr. Trump could still waive them if he certified that it was necessary for national security reasons. Negotiators also added requirements that the administration regularly report to Congress on how the penalties were being carried out.

Senators also said they had adjusted language governing the bill’s secondary tariffs to exempt American allies that still purchase small amounts of oil, gas and other energy from Russia if they were demonstrably reducing their reliance on Russian-produced energy.

Mr. Blumenthal, who had worked with Mr. Graham on the measure for more than a year, said he was confident the changes would secure enough backing to overcome any objections from Democrats and yield the votes necessary for the measure to move ahead.

“We’ve got a solid core of 60-plus senators,” Mr. Blumenthal said.